-x^2-14x+14=0

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Solution for -x^2-14x+14=0 equation:


Simplifying
-1x2 + -14x + 14 = 0

Reorder the terms:
14 + -14x + -1x2 = 0

Solving
14 + -14x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-14 + 14x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 14x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 14x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 14x + x2 = 0 + 14
14x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
14x + x2 = 14

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 14 + 49

Reorder the terms:
49 + 14x + x2 = 14 + 49

Combine like terms: 14 + 49 = 63
49 + 14x + x2 = 63

Factor a perfect square on the left side:
(x + 7)(x + 7) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + 7) equal to 7.937253933 and -7.937253933.

Subproblem 1

x + 7 = 7.937253933 Simplifying x + 7 = 7.937253933 Reorder the terms: 7 + x = 7.937253933 Solving 7 + x = 7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.937253933 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.937253933 + -7 x = 7.937253933 + -7 Combine like terms: 7.937253933 + -7 = 0.937253933 x = 0.937253933 Simplifying x = 0.937253933

Subproblem 2

x + 7 = -7.937253933 Simplifying x + 7 = -7.937253933 Reorder the terms: 7 + x = -7.937253933 Solving 7 + x = -7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.937253933 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.937253933 + -7 x = -7.937253933 + -7 Combine like terms: -7.937253933 + -7 = -14.937253933 x = -14.937253933 Simplifying x = -14.937253933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.937253933, -14.937253933}

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